To put the matter in simple terms, we know that aircraft horizontal stabilisers are aerodynamic surfaces in a typically trapezoid form whose leading edge is typically virtually straight (but not necessarily), and often fitted with control surface(s) on the trailing edge. On large aircraft, the horizontal stabiliser usually also has a feature whereby the leading edge moves vertically (as the stabiliser is rotated relative to the aircraft fuselage), which improves the aircraft's flight and general performance characteristics. On small aircraft, the leading edge of the horizontal stabiliser is often fixed.
The horizontal stabiliser is an aerodynamic surface whose purpose is to ensure good flying qualities (stability, handling and balance) in all flying conditions.
However its very existence creates aerodynamic drag, which acts negatively on the aircraft's performance.
In order to improve this performance, we can try to reduce the surface area of the horizontal stabiliser, but without degrading the aircraft's flying qualities.
We know that on the majority of short-haul aircraft of the “under wing” engine type, several criteria are used to dimension the surface of the horizontal stabiliser depending on the position of the aircraft's centre of gravity, namely:                balance criteria (the horizontal stabiliser must always be able to guarantee the desired attitude of the aircraft):            a) the ability to balance the aircraft throughout its flight envelope with a forward centre of gravity;    b) the ability to balance the aircraft throughout its flight envelope with an aft centre of gravity;            stability criteria (the aircraft must remain stable whatever the flight phase):            c) the point of manoeuvre: the aircraft's limit of stability with an aft centre of gravity; and            handling criteria (the aircraft must be able to provide the pitch necessary for carrying out the desired manoeuvres):            d) the so-called “pushover” manoeuvre, at forward centre of gravity during which the horizontal stabiliser experiences extremely negative angles of attack (aircraft pitch nose down); and    e) the so-called “CEV” manoeuvre, at aft centre of gravity during which the horizontal stabiliser experiences extremely positive angles of attack (aircraft pitch nose up).
These criteria can be classified into two categories: linear criteria and non-linear criteria. More precisely:                criteria a) and b) are directly governed by the linear gradient of the horizontal stabiliser at a fixed angle of attack and given by the minimum and maximum deflection of the said horizontal stabiliser. At this given angle of attack, the steeper the gradient, the more lift is created in absolute value and the more the criterion is improved; and        criterion c) mentioned above is a stability criterion, which is also directly linked to the linear efficiency of the horizontal stabiliser. The steeper this gradient, the more significant stability becomes and the less the criterion is critical to dimensioning.        
In addition, the linear efficiency of the horizontal stabiliser is defined by its planform, principally by its aspect ratio and its sweep angle.
Furthermore, criteria d) and e) call on non-linear characteristics of the plane. This means that the “pushover” manoeuvre is linked to stalling of the horizontal stabiliser at negative angles of attack. As far as the “CEV” manoeuvre is concerned, this is deduced from the maximum positive lift that the horizontal stabiliser is capable of providing with a positive deflection of the control surface.
These non-linear and stalling characteristics are mainly linked to the aerodynamic profiles used. The angles of attack for stalling are also sensitive to the linear characteristics of the plane.
The fact of increasing the efficiency of the horizontal stabiliser leads to a degradation of the angles of attack for stalling the stabiliser surface. The linear and non-linear characteristics therefore act against each other and the effect on the size of the horizontal stabiliser is virtually neutral (i.e. no increase in CLmax).
In addition, to be able to reduce the size of the horizontal stabiliser, we need to improve the non-linear characteristics of the stabiliser surface while keeping the linear characteristics (and therefore the planform) constant.